Формулы - Производные и интегралы

1.

0dx C

10.

sin xdx cos x C

dx

1

x

19.

arctg

C

a2 x2

a

a

2.

dx x C

11.

cos xdx sin x C

20.

dx

arcsin x C

1 x2

3.

xn dx

xn 1

C

12.

tgxdx ln

cos x

C

21.

dx

arcsin

x

C

a

n 1

a2 x2

4.

dx

1 1

C

13.

ctgxdx ln

sin x

C

22.

dx

1

ln

x a

C

xn

n 1

xn 1

x2

a2

2a

x a

dx

dx

ctgx C

dx

1

a x

5.

2

x C

14.

23.

ln

C

sin2 x

a2

x2

2a

a x

x

dx

dx

dx

6.

ln

x

C

15.

tgx C

24.

ln

x

x2

a2

C

x

cos2

x

x2 a2

dx

1

dx

x

dx

7.

ln

ax b

C

16.

ln

tg

C

25.

ln

x

x

2

a

2

C

ax b

a

sin x

2

x2 a2

a

x

dx

x

ax dx

C

17.

ln

C

f (x)

dx ln

f (x)

C

8.

tg

26.

f (x)

ln a

cos x

4

2

x

x

dx

df (x)

9.

e

dx e

C

18.

arctgx C

27.

ln

f (x)

C

1 x2

f (x)

1.

0

1

1

(C)

1. (C u(x))

u (x)

7. (loga x)

13.

(ctgx)

x ln a

sin2 x

2.

1

8. (e

x

) e

x

1

(x)

14.

(arcsin x)

2. (C u(x))

C u (x)

x2

1

3.

(x

n

) nx

n 1

9. (a

x

) a

x

ln a

1

15.

(arccos x)

3. (u v)

u

v

1 x2

1

cos x

1

4.

(

x )

16.

(arctgx)

1 x2

2 x

1

1

sin x

1

u v uv

5.

(

)

11. (cos x)

17.

(arcctgx)

5. (

u

)

x

x2

1

x2

v

v2

6.

(ln x)

1

1

( f (g(x))) f (u) g (x)

x

12. (tgx) cos2 x

u

x